Space-charge Waves Research Articles

Nonlinear time-dependent simulation of helix traveling wave tubes

A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory.

The evolution of a modulated electron beam in a dense plasma barrier

The dynamics of a modulated electron beam in a plasma barrier is studied via computer simulations using the 1D and 2D models for a wide range of parameters, such as initial beam modulation depth, electron beam current density and plasma density profile. The effects of competition between the resonant mode of a beam–plasma system and space charge wave of the beam at the modulation frequency are discussed. The influence of the beam–plasma turbulence mode on the evolution of the modulated beam is studied. The evolution of the velocity distribution function of the modulated beam during its motion in the dense plasma is considered, and the influence of background plasma inhomogeneity on the modulated beam evolution is also studied. For 2D simulation the influence of the beam transversal restriction is discussed. The simulation results are compared with previous laboratory experiments.

Suppression of In-Band Power Holes in Helix Traveling-Wave Tubes

Slow-wave structures employed in forward-wave linear beam amplifiers such as wideband helix traveling-wave tubes (TWTs) always support backward waves. A backward-wave space harmonic of a signal at a harmonic of a drive signal can effectively interact with a slow space-charge wave of an electron beam. In this case, the backward wave can compete with a forward wave, which results in backward-wave oscillation (BWO) power holes under large signal conditions. Sufficiently large power holes have serious consequences for the performance of a system in which the TWT is employed. In this paper, we report a study of BWO power holes simulated using a 2.5-D large signal helix TWT code and demonstrate an effective method, the pitch step method, to suppress BWO power holes.

Orientational dependencies of space-charge waves under the action of a magnetic field in GaAs:Cr

Space-charge wave (SCW) excitation is studied under the influence of an external magnetic field in GaAs:Cr depending on the orientational angle of the exciting oscillating sinusoidal interference pattern to the external electric field. It was found that the tilt of the SCW propagation direction induced by the magnetic field results in a shift of the orientational dependence curve. This feature allows determining the deviation angle of charge carriers’ trajectory and their sign. A quantitative theoretical explanation of the effects is proposed and a theoretical expression for the SCW ac-current is given.

Numerical simulation of amplification of space charge waves in n-InP films

a b s t r a c t The non-linear interaction of space charge waves including the amplification in microwave and millimeter wave range in n-InP films, possessing the negative differential conductance phenomenon, is investigated theoretically. Both the amplified signal and the generation of harmonics of the input signal are demon- strated, which are due to non-linear effect of the negative differential resistance. It is possible to observe an amplification of the space charge waves in n-InP films of submicron thicknesses at essentially higher frequencies f <70 GHz, when compared with n-GaAs films f < 44 GHz. The increment observed in the gain is due to the larger dynamic range in n-InP than in n-GaAs films. © 2011 Elsevier B.V. All rights reserved.

Numerical simulations of space charge waves in InP films and microwave frequency conversion under negative differential conductivity

Numerical simulations of amplification and propagation of space charge waves in InP films is investigated theoretically. A microwave frequency conversion using the negative differential conductivity phenomenon is carried out when the harmonics of the input signal are generated. An increment in the amplification is observed in n-InP films at essentially higher frequencies f&amp;lt;70 GHz, when compared with n-GaAs films f&amp;lt;44 GHz. This work provides a way to achieve a frequency conversion and amplification of micrometer and millimeter waves.

A three-dimensional time-dependent theory for helix traveling wave tubes in beam-wave interaction

This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beam-wave interaction. The radio frequency electromagnetic fields are represented as the superposition of azimuthally symmetric waves in a vacuum sheath helix. Coupling impedance is introduced to the electromagnetic field equations' stimulating sources, which makes the theory easier and more flexible to realize. The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations. The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included. The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields, focusing fields and space-charge fields. The numerically simulated results of a tube are presented.

Influence of Nonlocality on Amplification of Space Charge Waves in n-GaN Films

It is investigated theoretically the amplification of space charge waves (SCWs) due to the negative differential conduc-tivity (NDC) in n-GaN films of submicron thicknesses placed onto a semi-infinite substrate. The influence of the nonlo-cal dependence of the average electron velocity on the electron energy is considered. The simplest nonlocal model is used where the total electron concentration is taken into account. The relaxation momentum and energy frequencies have been calculated. The influence of the nonlocality on NDC results in the decrease of the absolute value of its real part and appearance of the imaginary part. The calculation of the diffusion coefficient leads to essential errors. The simulations of spatial increments of the amplification of SCWs demonstrate that the nonlocality is essential at the fre-quencies f ? 150 GHz, and the amplification is possible up till the frequencies f ? 400 ??? 500 GHz.

Study on the dispersion relations of a relativistic annular electron beam guided by a finite axial magnetic field

The relativistic annular electron beam guided by a finite axial magnetic field is studied in this paper, in which the electron beam is considered as a special media. Making use of the constitutive transformation and the Lorentz transformation in the four-dimensional space, the permittivity tensor of the stationary magnetized plasma, the permittivity tensor, the permeability tensor and the chiral tensor of the electron beam in the rest (laboratory) frame are acquired. And the boundary conditions, including the surface current density due to the ripple of the beam, have been obtained. As an example of the applications of this approach, the dispersion relations of a relativistic annular electron beam guided by a finite axial magnetic field in a waveguide has been studied. The results of numerical calculation show that the present approach is more accurate and can provide clearer mode information for the electron beam. In addition, the results also show the axial magnetic field can affect the dispersion curves of space charge wave via the surface current density of an electron beam. Thus this approach can be exploited in a number of electron beam-wave interaction systems, including some kinds of free electron devices, plasma filled Cherenkov radiated free electron lasers and masers.

Transit time instabilities in an inverted fireball. II. Mode jumping and nonlinearities

A fireball is formed inside a highly transparent spherical grid immersed in a dc discharge plasma. The ambient plasma acts as a cathode and the positively biased grid as an anode. A strong nearly current-free double layer separates the two plasmas. Electrons are accelerated into the fireball, ionize, and establish a discharge plasma with plasma potential near the grid potential. Ions are ejected from the fireball. Since electrons are lost at the same rate as ions, most electrons accelerated into the fireball just pass through it. Thus, the electron distribution contains radially counterstreaming electrons. High-frequency oscillations are excited with rf period given by the electron transit time through the fireball. Since the frequency is well below the electron plasma frequency, no eigenmodes other than a beam space-charge wave exists. The instability is an inertial transit-time instability similar to the sheath-plasma instability or the reflex vircator instability. In contrast to vircators, there is no electron reflection from a space-charge layer but counterstreaming arises from spherical convergence and divergence of electrons. While the basic instability properties have been presented in a companion paper [R. L. Stenzel et al., Phys. Plasmas 18, 012104 (2011)], the present paper focuses on observed mode jumping and nonlinear effects. The former produce frequency jumps and different potential profiles, the latter produce harmonics associated with electron bunching at large amplitudes. In situ probe measurements are presented and interpreted.

Analyses for the stability of multi-gap Hughes-type coupled cavity

In this paper, the analytical expressions of the beam-wave coupling coefficient and the beam-loaded conductance in the N-gap Hughes-type coupled cavity used in an extended- interaction klystron are derived based on the space-charge wave theory. The stability of the circuit is discussed through calculating the quality factor of the electron beam. The theoretical analyses show that with the increase of N, the stability of operating mode (2π) becomes more sensitive to the beam voltage, and that the parasitical oscillation may more easily occur and is difficult to suppress. In addition, the increase of the perveance and the decrease of the external loaded quality factor may both cause the instability of the system. The electric field intensities on the gap are greatly different among the modes 2π, π and π/2, which may be a new subject for improving the power capability and the bandwidth in klystron development.

Beam-wave synchronization and coupling in a multi-gap coupled cavity

The analytical expressions of the beam-wave coupling coefficients and the beam-loaded conductance in an N-gap coupled cavity are derived based on space-charge wave theory. Through calculating the relations of the beam-wave coupling coefficient and the normalized beam-loaded conductance to the gap number, beam voltage and perveance for 2π mode, the mechanism of the beam-wave synchronization and coupling in the multi-gap coupled cavity are discussed. The results show that, with the increase of N(≥2), the beam-wave coupling efficiency and the normalized beam-loaded conductance vary with beam voltage more rapidly and there is a maximum value for the absolute squared value of the coupling coefficient |MN|2 and a maximum value and a minimum value for the normalized beam-loaded conductance gb. The magnitudes of these extrema increase with the increase of gap number N, and the corresponding voltage is close to the synchronization voltage. The increase of the perveance could make the voltage difference between two extremums of gb increase, the magnitudes of these extrema decrease, and the beam-wave coupling efficiency fall.

Traveling waves in a free-electron laser with an electromagnetic wiggler

The propagation of electromagnetic traveling wave in a free-electron laser (FEL) with an electromagnetic wiggler is investigated using the relativistic fluid-Maxwell formulation. By adapting the traveling-wave ansatz, three coupled, nonlinear ordinary differential equations are obtained describing the nonlinear propagation of the coupled wave. These equations may be used to study saturation in FELs. By linearizing the nonlinear equations dispersion relations for the traveling wave are obtained. Numerical solution of the small-signal traveling dispersion relation reveals the coupling of radiation to both slow and fast space-charge waves. It is shown that the traveling wave, which is not a normal mode in a laboratory frame, becomes a normal mode in terms of a transformed variable.

Space-charge waves in a relativistic electron beam with ion-channel guiding

AbstractSpace-charge waves in a relativistic electron beam that completely fills a cylindrical metallic waveguide and is guided by an ion channel are analyzed numerically. Equilibrium consists of a uniform and rigid rotation without betatron oscillations. Using cold fluid equations a differential equation and boundary conditions are derived that constitute an eigenvalue problem. This eigenvalue problem is solved, numerically, with the finite difference scheme using shooting method. Dispersion characteristics and electrostatic potential structures of azimuthally symmetric and nonsymmetric space-charge waves are studied. Perfect agreement with analytical results at asymptotic limit of zero axial velocity is found. It was found that relativistic effects modify the dispersion characteristics of the space-charge waves considerably and can concentrate the electric field energy of the wave into a thin and small shell around the axis.

Free electron laser with bunched relativistic electron beam and electrostatic longitudinal wiggler

The system of the nonlinear nonstationary equations describing spatial-temporal dynamics of the amplitudes of an undulator radiation and a space charge wave of a relativistic electron beam in the resonator is obtained. The electrostatic longitudinal wiggler is considered. A bunch of the electron beam injects to the resonator, at the ends of which two mirrors are placed. After the interaction of electrons of bunch with radiation in the presence of wiggler and after amplifying electromagnetic pulse, a part of radiation is reflected back by semitransparent mirror. Then, it reaches to the initial of the system where the other mirror is placed. Synchronously, when the pulse is reflecting, the other electron bunch enters to the resonator and interacts with the pulse. This operation has simulated until saturation of growth of the electromagnetic pulse. The dynamics of the problem is simulated by the method of macro particles. The dynamics of pulse amplification, motion of the electrons, and spectra of output radiation in each stage are simulated.

Dispersion characteristics of the electromagnetic waves in a relativistic electron beam guided by the ion channel

In this article, the dispersion characteristics of the paraxial (near axis) electromagnetic (EM) waves in a relativistic electron beam guided by the ion channel are investigated. Equilibrium fields such as ion-channel electrostatic field and self-fields of relativistic electron beam are included in this formalism. In accordance with the equilibrium field structure, radial and azimuthal waves are selected as base vectors for EM waves. It is shown that the dispersion of the radially polarized EM and space charge waves are influenced by the equilibrium fields, but azimuthally polarized wave remain unaffected. In some wave number domains, the radially polarized EM and fast space charge waves are coupled. In these regions, instability is analyzed as a function of equilibrium structure. It is shown that the total equilibrium radial force due to the ion channel and electron beam and also relativistic effect play a key role in the coupling of the radially polarized EM wave and space charge wave. Furthermore, some asymptotic behaviors such as weak and strong ion channel, nonrelativistic case and cutoff frequencies are discussed. This instability could be used as an amplification mechanism for radially polarized EM waves in a beam-plasma system where a relativistic electron beam is guided by the ion channel.

Experimental study of large-amplitude perturbations in space-charge dominated beams

Detailed experimental measurements are presented concerning the propagation of space-charge waves of varying amplitudes in an intense, charged-particle beam. A short perturbation to the density profile is applied at the electron gun, and both current and mean energy profiles are measured at two locations downstream. The measurements are compared to predictions of a linear 1D cold-fluid model, and self-consistent particle-in-cell simulations. For sufficiently small perturbation amplitudes, the experiment, simulation, and 1D theory agree. For larger amplitudes, the simulation begins to diverge from theoretical predictions due to nonlinear effects. Experimental observations for large-amplitude perturbations differ markedly from either theory or simulation. With the aid of simulations with mismatched and misaligned beams, this departure of experiments from predictions is demonstrated to be caused by the loss of beam current due to scraping aided by the larger radius of the perturbation.

A time-dependent theory for helix traveling wave tubes in beam-wave interaction

A time-dependent theory for helix traveling wave tubes in beam-wave interaction is presented. The effect of wave on electrons is described by radio frequency (RF) field equations and space charge (SC) field equations, while the effect of electrons on waves is described by electron dynamic equations. The RF field equations are achieved from Ampere’s law and Faraday law, combined with sheath helix model RF field. The SC field equations are achieved from a space charge wave model. The electron dynamic equations are achieved by substituting the RF field equations and the SC field equations into the Lorenz force equation. Using coupling impedance to treat exciting sources of RF field equations, the RF and the SC field equations can be solved with the help of high frequency simulation software, such as HFSS or HFCS, which makes this time-dependent theory more flexible. The feasibility of this theory is proved by numerical simulation.

Mode Coupling in a Partially Filled Plasma Waveguide With a Dielectric Liner

The stimulated Raman scattering of a perturbed TM mode in a dielectric loaded partially filled plasma waveguide is considered. The radiation is the result of the scattering of pump electromagnetic wave, which is an EH waveguide mode, off of a space-charge wave. A nonlinear wave equation for a three-wave interaction is used to investigate the coupling of the space-charge and waveguide modes. Dispersion relations for electromagnetic modes are solved numerically to study the frequency characteristics of the interaction of the EH waveguide modes with the space-charge modes. Formulas for the growth rates of the backscattered wave near the electron cyclotron frequency are derived, and the effect of a dielectric liner on the growth rates is investigated. Numerical studies show that the presence of the dielectric liner has an effect on the phase-matching condition and leads to rather larger growth rates close to electron cyclotron resonance.

Nonlinear Interactions of Space Charge Waves

Nonlinear Interactions of Space Charge Waves